Other Topics

Related Sites

Section Information

The Distribution in X-Ray Class of Solar Flares

For some prediction purposes it is useful to know how many X-ray flares
of a given energy might be expected. For example, if the predicted
yearly sunspot number for 1994 is 30, how many flares of class M1-2 or
X1-2 might be expected during the year. These sort of estimates have particular
value when combined with other information to yield estimates of fadeout effects
on HF circuits.

The following equations are useful in making such estimates.
The first, derived from flare data between 1976 and 1991, connects
sunspot number R12 and the total number of M Class
flares (Nm) in a year:

Nm = 2.86 R12

There is a similar relationship, but between sunspot
number and the total number of X Class flares in a year:

Nx = 0.23 R12

Another equation gives the distribution of flares in X-ray class
as derived from flare data from 1976 to mid 1993:

N = Nm DELTA 1.26 X-2.12

where:

X is the X-ray class measured as 1.0 for M1, 5.0 for M5, and 10.0 for X1 and so on

N is the expected number of flares in a range DELTA centred on an X-ray class of X

To calculate the number of flares in a range M1-2, the above equation
can be used with X = 1.5 and DELTA = 1.0. Similarly, for a range
X1-2, X = 15 and DELTA = 10.

The figure below shows flare occurrence plotted against X-ray class, indicating that
the third of the above equations gives a good fit right from class M1 through to X5.

It should be stressed that the equations above are statistical
in nature whilst flares, even at solar minimum, come in clumps where the
expected yearly occurrence may be produced within several weeks. Nevertheless,
in the absence of more detailed knowledge, the equations produce estimates
which are useful for planning purposes. Naturally, the random nature of
flares is more apparent and the equations less useful, when
short time intervals are used.